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# If the 4th,10th and 16th terms of a G.P. are x,y and z, respectively. Prove that x,y,z are in G.P.

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#### Let a be the first term and r be the common ratio of the G.P.According to the given condition,a4=ar3=x...(1)a10=ar9=y...(2)a16=ar15=z...(3)Dividing (2) by (1), we obtainyx=ar2r3⇒yx=r6Dividing (3) by (2), we obtainzy=ar15ar9⇒zy=r6∴yx=zyThus, x, y, z are in G.P.

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